Boris Johnson's former communications chief threatened to use his contacts in the press to confront the BBC over its coverage of the Conservative mayor of London, suggesting that "good friends in No 10" could also be deployed against them, emails leaked to the Guardian reveal.

The threat of a "huge public fight" was levelled at senior BBC figures by Guto Harri, a former BBC correspondent himself, who announced last week that he was moving to become director of communications at News International.

Harri's suggestion that Downing Street was also ready to put pressure on the public service broadcaster raises questions about the Tories' tactics against the BBC and the extent of the pressure City Hall has exerted in its attempts to influence coverage.

The revelation comes at the start of another crucial week of evidence to the Leveson inquiry into phone hacking, which is now focusing on the relationship between the press and politicians. The former prime minister Tony Blair will give evidence on Monday followed by five cabinet ministers: Michael Gove and Theresa May on Tuesday; Vince Cable and Ken Clarke on Wednesday; and on Thursday Jeremy Hunt, who is facing intensifying calls to resign over his handling of News International's bid for a controlling stake in BSkyB.

In the emails, Harri told Will Walden, the BBC's Westminster news editor – whom Johnson has since chosen as Harri's replacement as head of communications at City Hall – that the BBC faced a "huge public fight" if an interview about Johnson with his unauthorised biographer, Sonia Purnell, went ahead.

The email to Walden reads: "Dear Will. We are all sick of this at City Hall, and increasingly at Number 10. BBC London is in danger of causing real problems to all of us."

Pressing Walden on the question of who else he should raise his concerns with just minutes after raising it with two senior BBC figures in a separate email, he added: "If this interview run [sic] on Sunday, there'll be a huge public fight."

The interview with Purnell, whose book, Just Boris, was being published later that month, discussed Johnson's progress in office as mayor, his performance at the Conservative party conference held days earlier, and speculation about his future political ambitions beyond London.

Harri intimated that the public broadcaster would face a backlash from newspaper stables friendly to Johnson, as well as from Downing Street, if the item saw the light of day.

In a second email to Ric Bailey, the BBC's chief adviser for politics, and David Jordan, head of editorial policy and standards, late on the evening of Friday 7 October, Harri complained about the interview recorded that day in the presence of an employee of City Hall and due to be broadcast on the Sunday for the London segment of the lunchtime BBC Politics Show.

Highlighting an excerpt of the interview, which Harri claimed was "implying the mayor is 'losing his touch' because he 'failed' to upstage the PM", he criticised the decision to allow Purnell to "pontificate without challenge, qualification or allowing us a right to reply" and described the author as someone who "knows no one in No 10". He concluded: "Please please please sort this out. Or you leave me with no option but to use our friends in the papers to launch a public discussion about what this says about the BBC. And our good friends in No 10 are pretty trigger-happy too." Harri followed this up with his email to Walden 16 minutes later.

When contacted by the Guardian, Harri said: "It was my job at City Hall to ensure fair coverage for the mayoralty and I did what I could over four years to deliver that in a professional and courteous manner." He insisted his comments about No 10 were not a threat but merely reflected the broader frustrations he claims were felt not only inside City Hall but in "central government, the Olympic family and some within BBC London itself" about the "relentlessly hostile" coverage.

Johnson has since used his Daily Telegraph column to make strong criticisms of the BBC, arguing on 14 May that the next director general of the BBC must be a Conservative.

Quipping that he had just fought an election campaign "in which I sometimes felt that my chief opponent was the local [London] BBC news", Johnson wrote: "The prevailing view of Beeb newsrooms is, with honourable exceptions, statist, corporatist, defeatist, anti-business, Europhile and above all, overwhelmingly biased to the left.

"Of course they are: the whole lot of them are funded by the taxpayer." A BBC spokeswoman said: "It is not unusual to receive complaints before and after broadcast from people trying to influence our reporting and they are considered with our commitment to impartiality in mind. However all news output is judged on editorial merit, produced in an balanced way, in accordance with BBC editorial guidelines."